Permutation: n Different Things Taken All at a Time When All Are Not Different.

Q.

(i) How many different words can be formed by using all the letters of the word, 'ALLAHABAD'?

In how many of them :

(ii) Both L's do not come together ?

(iii) The vowels occupy the even positions ?

Q. Find the number of ways in which n distinct balls can be put into three boxes so that no two boxes remain empty

Q. 8.A bag contains 15 balls of which 6 are identical find the number of ways of selecting 8 balls.

Q. Five balls are to be placed in three boxes. Each box can hold all the five balls. In how many different ways can we place the balls so that no box remains empty, if balls and boxes both are identical is

Q. 36. Five balls of different colours are to be placed in 3 boxes of different sizes. Each box can hold all 5 balls. The number of ways of placing the balls in boxes so that no box remains empty i

Q. Words of length 10 are formed using the letters A, B, C, D, E, F, G, H, I, J. Let x be the number of such words where no letter is repeated and let y be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then, $\frac{y}{9x}=$___

Q. If all permutations of the letters of the word "AGAIN" are arranged as in dictionary, then fiftieth word is

1. NAAGI
2. NAAIG
3. NAGAI
4. NAIAG

Q. The number of $6$-digit numbers that can be made with the digits $0,1,2,3,4$ and $5$ so that even digits occupy odd places, is

1. $36$
2. $noneofthese$
3. $48$
4. $24$

Q. Number of permutations of three different things $A,B,C,D$ taking:-

1. 12
2. 24
3. 4
4. \N

Q.

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed ?

Q. An urn contains 7white, 5black and 3red balls. Two balls are drawn at random. Find the probablity that 1) both the balls are red2) one ball is white

Q. 6 boys are to sit around a round table. Number of ways for the same is

एक गोलाकार मेज के चारों ओर 6 लड़कों को बैठना है। उनके बैठने के तरीकों की संख्या है

1. 120
2. 240
3. 720
4. 1080

Q. How many different nine-digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions ?

1. 16
2. 36
3. 60
4. 180

Q. 19. Find the number of ways in which n distinct balls can be put into three boxes so that no two boxes remain empty

Q. The number of anagrams of the word ${}^{\prime }COLOURFU{L}^{\prime }$ is

1. $45359$
2. $45360$
3. $45361$
4. none of these

Q.

How many numbers are there between 100 and 1000 such that 7 is in the units place? (repetition of digits is allowed)

Q.

find the number of natural numbers from 1 to 1000 having none of their digits repeated?